# c ++ Sin和Cos

``double radians = DegreesToRadians( angle ); double cosValue = cos( radians ); double sinValue = sin( radians );` `

` `double DegreesToRadians( double degrees ) { return degrees * PI / 180; }` `

C / C ++提供了`sin(a)``cos(a)``tan(a)`等函数，它们需要一个带有弧度单位而不是度数的参数。 `double DegreesToRadians(d)`执行转换是接近，但近似的转换结果四舍五入。 机器的`M_PI`也接近，但与math上的无理数`π`不一样。

OP的`180`代码传递给`DegreesToRadians(d)` ，然后是`sin()/cos()` ，由于舍入， `double()`有限精度以及`PI`可能的弱值而给出的结果与预期不同。

` `#include <math.h> #include <stdio.h> static double d2r(double d) { return (d / 180.0) * ((double) M_PI); } double sind(double x) { if (!isfinite(x)) { return sin(x); } if (x < 0.0) { return -sind(-x); } int quo; double x90 = remquo(fabs(x), 90.0, &quo); switch (quo % 4) { case 0: // Use * 1.0 to avoid -0.0 return sin(d2r(x90)* 1.0); case 1: return cos(d2r(x90)); case 2: return sin(d2r(-x90) * 1.0); case 3: return -cos(d2r(x90)); } return 0.0; } int main(void) { int i; for (i = -360; i <= 360; i += 15) { printf("sin() of %.1f degrees is % .*e\n", 1.0 * i, DBL_DECIMAL_DIG - 1, sin(d2r(i))); printf("sind() of %.1f degrees is % .*e\n", 1.0 * i, DBL_DECIMAL_DIG - 1, sind(i)); } return 0; }` `

` `sin() of -360.0 degrees is 2.4492935982947064e-16 sind() of -360.0 degrees is -0.0000000000000000e+00 // Exact sin() of -345.0 degrees is 2.5881904510252068e-01 // 76-68 = 8 away // 2.5881904510252076e-01 sind() of -345.0 degrees is 2.5881904510252074e-01 // 76-74 = 2 away sin() of -330.0 degrees is 5.0000000000000044e-01 // 44 away // 0.5 5.0000000000000000e-01 sind() of -330.0 degrees is 4.9999999999999994e-01 // 6 away sin() of -315.0 degrees is 7.0710678118654768e-01 // 68-52 = 16 away // square root 0.5 --> 7.0710678118654752e-01 sind() of -315.0 degrees is 7.0710678118654746e-01 // 52-46 = 6 away sin() of -300.0 degrees is 8.6602540378443860e-01 sind() of -300.0 degrees is 8.6602540378443871e-01 sin() of -285.0 degrees is 9.6592582628906842e-01 sind() of -285.0 degrees is 9.6592582628906831e-01 sin() of -270.0 degrees is 1.0000000000000000e+00 // Exact sind() of -270.0 degrees is 1.0000000000000000e+00 // Exact ...` `

` `// cos(M_PI * -90.0 / 180.0) returns 0.00000000000000006123233995736766 //__cospi( -90.0 / 180.0) returns 0.0, as it should // #define degree2rad 3.14159265359/180 // #define degree2rad M_PI/ 180.0 // double rot = -degree2rad * ang; // double sn = sin(rot); // double cs = cos(rot); double rot = -ang / 180.0; double sn = __sinpi(rot); double cs = __cospi(rot);` `

` `/* __sinpi(x) returns the sine of pi times x; __cospi(x) and __tanpi(x) return the cosine and tangent, respectively. These functions can produce a more accurate answer than expressions of the form sin(M_PI * x) because they avoid any loss of precision that results from rounding the result of the multiplication M_PI * x. They may also be significantly more efficient in some cases because the argument reduction for these functions is easier to compute. Consult the man pages for edge case details. */` `